Why should the rotor speed of an ideal impulse stage be about half the speed of the incoming steam?

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In an ideal impulse stage, the rotor speed should be approximately half the speed of the incoming steam to achieve minimum exit kinetic energy.1

In this configuration, the steam's kinetic energy is extracted as it passes through the moving blades. Because there is no pressure drop within the blade passage, the magnitude of the steam's velocity relative to the blade remains constant. By setting the rotor velocity to half of the entering steam velocity, the absolute velocity of the steam leaving the blade is minimized, ensuring that the change in kinetic energy is fully converted into useful work.1